Consider the function f(x)= 6x cos(x) + 7 on the interval 0 ≤ x ≤ 1. The Intermediate Value Theorem guarantees that for certain values of k there is a number c such that f(c) = k. In the case of the function above, what, exactly, does the intermediate value theorem say? To answer, fill in the following mathematical statements, giving an interval with non-zero length in each case. For every k in the interval there is a c in the interval such that f(c) = k. ≤k≤
Consider the function f(x)= 6x cos(x) + 7 on the interval 0 ≤ x ≤ 1. The Intermediate Value Theorem guarantees that for certain values of k there is a number c such that f(c) = k. In the case of the function above, what, exactly, does the intermediate value theorem say? To answer, fill in the following mathematical statements, giving an interval with non-zero length in each case. For every k in the interval there is a c in the interval such that f(c) = k. ≤k≤
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the function f(x) = 6x - cos(x) + 7 on the interval 0 ≤ x ≤ 1. The Intermediate Value
Theorem guarantees that for certain values of k there is a number c such that f(c) = k. In the case
of the function above, what, exactly, does the intermediate value theorem say? To answer, fill in the
following mathematical statements, giving an interval with non-zero length in each case.
For every k in the interval
there is a c in the interval
such that f(c) = k.
<k<
se≤
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